Q. The sum of $n$ terms of the series $1 + (1 + x) + 1\left( 1 + x + x^{2} \right) + ...$ will be
A) $\frac{1 - x^{n}}{1 - x}$
B) $\frac{x\left( 1 - x^{n} \right)}{1 - x}$
C) $\frac{n(1 - x) - x\left( 1 - x^{n} \right)}{(1 - x)^{2}}$
D) None of these
Explanation
The correct answer is Option C: $\frac{n(1 - x) - x\left( 1 - x^{n} \right)}{(1 - x)^{2}}$.
A detailed explanation for this question is being prepared.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.